Q$1$

$(1)$ Two single$-$phase transformers A and B have the same rated voltage $\frac{220}{110}V$ and their highvoltage windings have the same number of turns. During open$-$circuit tests, their measured excitation currents have the relationship of $I_{OA}=2I_{OB}.$

$(1-1)$ Find the relationship of their reluctances. $(10)$

$(1-2)$ If the high$-$voltage windings are connected in series and supplied with $440$ V voltage, calculate their voltages of secondary sides respectively. $(20)$

$(2)$ Suppose that the stator of a synchronous generator is supplied with a three$-$phase symmetrical voltage source, and the supplied voltage is kept unchanged, compare, with brief explanation, the stator currents in the following two cases:

$($i$)$ the rotor is physically removed;

$($ii$)$ the rotor rotates at the rated speed with zero excitation current. $(10)$